Pentagram Spirals

2013/04/21 by Richard Evan Schwartz, Schwartz, Richard Evan · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #math.DS

paper · pdf · doi:10.48550/arxiv.1304.5708

50 pages. In this latest version, I corrected several typos, and mildly revised the paper according to the comments of a referee. The paper will soon be published in the Journal of Experimental Math

openalex publication_date 2013/04/21 · arxiv created 2013/07/19 · arxiv updated 2013/07/22 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on some of the deeper algebraic structure, such as the complete integrability of the associated dynamical system.

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